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Question

The weight of a light bulb has an average of 12.5 grs. with a standard deviation of 2.  Assume the variable is normally distributed.  If an inspector select randomly a sample of 30 bulbs ¿what is the probability of the weight of one bulb falls between 10 and 15 grs.?

Answer 1

To solve this problem, we will use the central limit theorem and the standard normal distribution.

First, we need to standardize the values of 10 and 15 using the formula:

z = (x - μ) / σ

where x is the value we want to standardize, μ is the mean of the population, and σ is the standard deviation of the population.

For x = 10: z = (10 - 12.5) / 2 = -1.25

For x = 15: z = (15 - 12.5) / 2 = 1.25

Next, we need to find the probability that a randomly selected bulb falls between these two values. This can be done by finding the area under the standard normal curve between z = -1.25 and z = 1.25.

Using a standard normal table or calculator, we can find that the area between these two values is approximately 0.6826.

Therefore, the probability of the weight of one bulb falling between 10 and 15 grs. is approximately 0.6826 or 68.26%.

Note: We assume that the sample of 30 bulbs is a random sample from the population, and that the sample size is large enough for the central limit theorem to apply.